Question

Solve the system, or show that it has no solution. If the system has infinitely many solutions,

express them in the ordered-pair form given in Example 6.

$\begin{array}{l}4x+2y=16\\ x-5y=70\end{array}$

Short answer

Hence, the solution of the system of equations $\begin{array}{l}4x+2y=16\\ x-5y=70\end{array}$is the ordered pair

Step-by-step solution

Step 1. Given information.

Given a system of equations$\begin{array}{l}4x+2y=16\\ x-5y=70\end{array}$

substitution method.

Step 2. Write down the concept.

Given equation,

$4x+2y=16$ …….(1)

$x-5y=70$ …….(2)

We are substituting equation (3) in equation (1),

$x=70+5y$ ……..(3)

Step 3. Determining the angle

We are substituting equation (3) in equation (1),

$\begin{array}{l}4(70+5y)+2y=16\\ 280+20y+2y=16\end{array}$

Subtracting 280 from both sides,

$22y=-264$

Dividing both sides by 22,

$y=-12$

Substituting the value of y in equation (3),

$\begin{array}{l}x=70+5(-12)\\ x=70-60\\ x=10\end{array}$